(a)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
the most populated rotational level for a sample of
(b)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
The most populated rotational level for a sample of
(c)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
The most populated rotational level for a sample of
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Chapter 14 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
- What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule given the following conditions: (i) the characteristic length is 10 nm and the volume in which the molecules are free to move is a cube with sides of 1 mm each. (ii) Only the first four rotational levels are accessible, but for some odd reason [to keep things simple] each state in each of those levels is equally populated. (iii) all molecules are in the ground vibrational state; (iv) the molecule has a triplet electronic ground level, like O2.arrow_forward4. Spectroscopic measurements indicate that the rotational constants of SO2, a non-linear molecule, are 2.02736, 0.34417, and 0.29354 cm-1. Note: kg = 0.69503476 cm-1/K. (a) Compute zrot at T= 350 K assuming its symmetry number is o= 2. Hint: Using the rotational temperatures for the molecule might make this easier. (b) At what temperature would the partition function equal 2.0 × 104?arrow_forward5. For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for J=0, 5, 10, 15, and 20. The rotational constant (B) is 3.83x10^-23 Joules.arrow_forward
- The three normal modes of water are the symmetric stretch (3652 cm¹), the antisymmetric stretch (3756 cm¹), and the bend (1595 cm¹). (a) Calculate the molecular vibrational partition function of water at 500 K. (b) At 500 K, what fraction of water molecules have the bend excited to v₂=1. What fraction of water molecules have the symmetric stretch excited to v₁=1? Why do more molecules have the bend excited? (c) At 500 K, what fraction of water molecules have both v2-1 and v₁=1 excited?arrow_forwardFor the equation 2K + Cl2------>2KCl. I understand Cl is diatomic , but where does the 2 in front of the K come from.arrow_forwardCalculate, and plot, the fraction of NO(g) molecules in each rotational state from l = 0-30 at 300 K and at 1000 K. Take the mass of N as 14 g/mol. Take the mass of O as 16 g/mol. The nitric oxide bond length is 116 pm.arrow_forward
- Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of helium gas, (ii) a sample of carbon monoxide gas, (iii) a solid sample of carbon monoxide, (iv) water vapour.arrow_forwardCalculate the vibrational and rotational temperatures (Ovib and Orot) for the diatomic molecular Lithium Hydride (LiH). The Li-H bond length is 0.1595 nm and the vibrational frequency (VL¡H) is 1405 cm'.arrow_forwardThe ground configuration of carbon gives rise to a triplet with the three levels 3P0, 3P1, and 3P2 at wavenumbers 0, 16.4, and 43.5 cm-1, respectively. (a) Eva luate the electronic partition function of carbon at (i) 10 K, (ii) 298 K, (b) Hence derive an expression for the electronic contribution to the molarinternal energy and plot it as a function of temperature. (c) Evaluate the expression at 25 °C.arrow_forward
- The rotational constant for the molecule 1H35Cl is B = 10.60 cm-1. Using Boltzmann statistics, determine the most likely rotational state J that such a molecule would be expected to have at a temperature of 300 K.arrow_forwardFor a specific molecule the ground state is nondegenerate while the first excited state is doubly degenerate. The excited state is removed from the ground state by 380 cm-1. What must the temperature of the system be for i) 25% and ii) 45% of the molecule to be in the first excited state?arrow_forward4. The following have to do with rotational partition functions. a) What are the symmetry numbers o for the following molecules? i) "Cl'CI ii) "CP"CI iii) triangular H3* iv) All isomers of C:H.F2 v) CH,CI vi) benzene b) Assume at = 10 the high temperature limit is reached. At what temperature does the high OR temperature limit become valid for: i) DBr (B = 4.24 cm') ii) F"CI (B = 0.516 cm') %3D iii) Csl (B = 0.236 cm) %3D e ) Obtain Jmax and / for the temperatures obtained in part b) and at 500 K.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,